Calculator
Stair Stringer Calculator
Cutting a stair stringer means notching a triangular pocket for every riser and tread out of a solid board, and every notch removes wood from the same side of the same piece of lumber. What's left behind the deepest point of that notch — the throat — is the only wood still carrying the stair's load at that point, and it's a genuinely different question from the rise-and-run layout that decides where the notches go in the first place.
This calculator lays out the stair from total rise and target dimensions the way a stair-layout tool does, but it goes a step further and computes the throat that's left after the deepest notch, against a minimum you set. A stringer with the right rise and run can still be structurally short if the board it's cut from wasn't deep enough to begin with, and that's the thing a plain rise-and-run calculation can't see.
Calculate your quantity
Finished floor to finished floor.
11-1/4 in actual for a 2x12.
Risers
14 risers
Riser height
7.714 in
- Treads
- 13 treads
- Total run
- 130 in
- Stringer length
- 14.08 ft
- Order length
- 16 ft
- Notch depth
- 6.108 in
- Throat remaining
- 5.142 in
- Stringers
- 4 stringers
- 2R + T comfort sum
- 25.43 in
- Stringer length along the cut line: 14 ft 1 in.
- A 11.25 in board leaves 5.14 in of throat after the notch, above the 3.5 in minimum.
- 2R + T is 25.43 in, outside the 24-25 in comfort range — the stair will feel steep or shallow underfoot.
Shopping summary
- • 4 stringers cut from 16 ft stock
- • 13 treads and 14 risers at 36 in wide
This is an estimate — confirm structural work with a professional.
How this calculation works
Risers come first, rounded to a whole number from total rise divided by a target riser height, and the actual riser height is then recalculated by dividing total rise by that whole number of risers — so every riser on the stair ends up exactly equal, even if that means each one lands a little off the target you entered. Treads are one fewer than risers, since the top riser is the floor above rather than a separate tread, and total run follows from tread count times tread run.
The throat calculation is separate from that layout math. It treats the notch as a right triangle with the riser height and tread run as its two legs, finds the perpendicular distance from that triangle's hypotenuse to the board's outer corner, and subtracts that notch depth from the board's actual depth. What's left is the throat — the continuous, uncut thickness of wood running the full length of the stringer below every notch — and it's this number, not the board's nominal size, that a stringer's structural capacity actually depends on.
- A deeper board (2x12 rather than 2x10) doesn't just look sturdier — it directly adds to the throat, inch for inch, since the notch geometry stays the same regardless of board depth.
- A steeper stair (taller risers relative to tread run) cuts a deeper notch for the same board, because the notch depth is set by the riser-and-run triangle, not by the board alone.
- Stringer count is set from stair width and spacing plus one extra stringer, since a run of stringers at N-inch centers across a given width needs one more stringer than the number of spaces between them.
- The 2R + T comfort figure — twice the riser height plus the tread run — is a separate check from the throat; a stair can pass one and fail the other, and both are reported independently.
The formula
notchDepth = (riserHeight x treadRun) ÷ sqrt(riserHeight² + treadRun²); throat = stringerDepth − notchDepth
- riserHeight
- Total rise divided by the whole number of risers the stair rounds to — recalculated after rounding so every riser on the stair is identical, rather than one odd riser absorbing whatever total rise didn't divide evenly.
- notchDepth
- The perpendicular distance from the notch's hypotenuse (the line connecting the riser-height point to the tread-run point) to the stringer's outer corner — the actual amount of board material the notch removes at its deepest point, which is less than either the riser height or the tread run alone.
- throat
- Stringer board depth minus notch depth — the continuous wood left below every notch along the stringer's full length. This is the dimension that carries load; a shallow throat is a structurally weak stringer even if the rise and run are both correct.
- stringers
- Stair width divided by on-centre spacing, rounded up, plus one — the number of parallel notched boards the stair needs, since stringers bound the spaces between them rather than sit only at the spacing interval itself.
- 2R + T
- Twice the riser height plus the tread run, in inches — a long-standing stair-comfort rule of thumb, independent of the throat calculation, that flags a stair as likely to feel too steep or too shallow underfoot rather than structurally unsound.
Throat and comfort are two unrelated checks that this page reports side by side on purpose: a stair can have a perfectly comfortable 2R + T sum and still be cut from too shallow a board, or have a generous throat on a stair that's uncomfortably steep to climb. Neither one substitutes for the other.
Where these numbers come from
- A minimum throat around 3.5 in as a commonly cited default
- A commonly cited residential minimum net thickness for a notched 2x stringer, reflecting what most jurisdictions expect to be left after cutting the deepest notch. Treat this as a typical starting default to check against, not a substitute for your specific local code, which the calculator's default matches but does not enforce or guarantee.
- The 2R + T comfort range of roughly 24 to 25 in
- A long-standing stair-design rule of thumb (a variant of what's often called Blondel's formula), widely cited in stair-building references as a proportion most people find comfortable to climb. It is a design convention, not a code requirement, and some codes instead specify riser and tread dimensions directly rather than this combined figure.
- 16 in on-centre stringer spacing as the common default
- A common residential framing convention for stringer spacing, mirroring standard joist and stud spacing; 12 in on-centre is also commonly used for wider stairs or where a heavier finish load is expected. Actual required spacing depends on tread thickness, span, and load, which local code governs.
Worked examples
A standard interior stair cut from 2x12 stock
| Total rise | 108 in |
|---|---|
| Target riser height | 7.5 in |
| Tread run | 10 in |
| Stair width | 36 in |
| Stringer spacing | 16 in on-centre |
| Stringer board depth | 11.25 in |
| Minimum throat | 3.5 in |
| Risers | 14 risers |
|---|---|
| Riser height | 7.714 in |
| Treads | 13 treads |
| Total run | 130 in |
| Stringer length | 14.08 ft |
| Order length | 16 ft |
| Notch depth | 6.108 in |
| Throat remaining | 5.142 in |
| Stringers | 4 stringers |
| 2R + T comfort sum | 25.43 in |
A 108 in floor-to-floor rise splits into 14 risers of 7.71 in each, and on a real 11.25 in deep 2x12, the notch for that rise and a 10 in tread run only cuts 6.11 in deep — leaving 5.14 in of throat, well clear of the 3.5 in minimum with room to spare. This is a comfortably over-built stringer from a structural standpoint.
The comfort check tells a slightly different story: at 25.43, the 2R + T sum sits just outside the 24-25 in range, meaning this exact riser-and-run combination will read as a hair steep underfoot even though nothing about it is unsafe. A small adjustment to tread run — closer to 10.6 in rather than 10 — would bring it inside the comfort range without changing the riser count or the throat at all.
A shallow deck stair cut from 2x10 stock on tighter spacing
| Total rise | 32 in |
|---|---|
| Target riser height | 7 in |
| Tread run | 12 in |
| Stair width | 48 in |
| Stringer spacing | 12 in on-centre |
| Stringer board depth | 9.25 in |
| Minimum throat | 3.5 in |
| Risers | 5 risers |
|---|---|
| Riser height | 6.4 in |
| Treads | 4 treads |
| Total run | 48 in |
| Stringer length | 4.81 ft |
| Order length | 6 ft |
| Notch depth | 5.647 in |
| Throat remaining | 3.603 in |
| Stringers | 5 stringers |
| 2R + T comfort sum | 24.8 in |
A short exterior run like this — 32 in of total rise over just 5 risers — lands almost exactly inside the comfort range at 24.8, a wide, shallow stair typical of a deck's approach. But swap the board down to a real 9.25 in deep 2x10 for this wider tread run and the throat comes out to only 3.6 in, just a tenth of an inch clear of the 3.5 in minimum entered here.
That's the pairing worth noticing: a comfortable, easy-climbing stair and a structurally marginal one, on the same set of numbers. A wider tread run cuts a deeper notch for the same riser height, and a shallower board gives that notch less to work with — either one alone might have passed with margin, and together they leave almost none. Stepping up to a 2x12 here, or tightening the tread run slightly, restores real margin without changing the stair's comfort.
Common mistakes
- Checking only the riser and tread dimensions and assuming any board deep enough to notch is automatically strong enough. The throat is a separate, load-bearing dimension that a rise-and-run layout alone doesn't calculate.
- Using nominal board depth (a '2x10 is 10 inches') instead of actual dressed depth (9.25 in) when checking the throat. That difference alone can be the gap between passing and failing a throat minimum.
- Widening the tread run to make a stair feel easier to climb without re-checking the throat. A deeper notch comes with a more comfortable run on the same riser height, and the two checks can pull in opposite directions on the same board.
- Assuming a housed or engineered stringer needs the same solid-throat minimum as a cut stringer. A housed stringer carries load differently, through the full board thickness with treads let into dadoes rather than sitting on a notch, and isn't subject to the same throat check at all.
- Treating the frost-depth-independent footingDepth-style local figures as something this page already knows. Local minimum throat requirements, like frost depth on a footing, vary by jurisdiction, and the default here is a starting point to verify, not a substitute for checking.
Shopping summary
Order stringer stock to the rounded length this page reports, in a board depth deep enough to clear your local throat minimum at the riser and run you're cutting — checking that before buying is far cheaper than discovering a shallow throat after the first stringer is already notched.
If the stair lands on a deck rather than an interior floor, the deck footing calculator sizes the post and footing the stair's own landing typically needs, and the deck board calculator covers the treads themselves once the stringers are set.
FAQ
What exactly counts as the throat, and where on the stringer is it measured?
It's the narrowest continuous band of uncut wood running the length of the stringer, measured perpendicular to the board's edge at the point where the notch cuts deepest — effectively at every riser-and-tread corner along the stringer, since each notch cuts the same depth on a stair with equal risers and runs.
Does adding a middle stringer fix a marginal throat?
No — an extra stringer reduces how far apart the stringers are spaced and how much a tread has to span between them, which is a separate concern from whether any single stringer's own throat is thick enough to carry load along its length. A marginal throat needs a deeper board or a different rise-and-run combination, not more stringers.
Why does the same stringer depth give a different throat on two different stairs?
Because notch depth depends on the riser-and-run triangle, not on the board alone — a steeper stair (taller risers relative to run) or a wider tread run each cut a deeper notch out of the same board, leaving less throat behind even though the board itself didn't change.
Is a housed stringer a way around a tight throat minimum?
Housed stringers — where treads and risers sit in routed dadoes rather than on a cut notch — don't lose the same wedge of material a cut stringer does, so they're a genuine option where a cut stringer's throat comes up short on an otherwise fixed rise-and-run layout. They're a different construction method with their own requirements, not simply a cut stringer built differently.
How much does order length change if I need a landing partway up?
This calculator assumes one continuous run from floor to floor; a landing splits that into two separate stringer runs, each with its own total rise and its own throat check, and the two runs are not simply half the length of a single continuous one because each needs its own top and bottom framing allowance.
Why is 3.5 in the default minimum throat rather than a larger, more conservative number?
It reflects a commonly cited residential default, not the most conservative figure available — some jurisdictions or engineered designs call for more. Raising the minThroat field to whatever your local code or a structural engineer specifies is the intended way to use this page for a stricter requirement, rather than treating the default as universally sufficient.
Where to go next
The projects this number is a step of, the guides that explain the method behind it, and the rest of its trade group.